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A224397 Number of possibilities of getting a prime sum when rolling n six-sided dice. 1
0, 3, 15, 73, 432, 2466, 12690, 67628, 395896, 2378907, 14778790, 93389066, 562139796, 3163874871, 17458695226, 100299771120, 608013094016, 3788103579016, 23633567094114, 145391247840963, 873481016484060, 5103300936908811, 29074526437910272, 163299878621689106 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Possibilities are counted "with repetition", i.e., rolling 2+3 and 3+2 counts as two possibilities. Otherwise said, the probability of getting a prime sum when rolling n six-sided dice, multiplied by 6^n.

LINKS

Giovanni Resta, Table of n, a(n) for n = 0..120

C. Rivera, Puzzle 684 - Primes in N dice.

MATHEMATICA

a[n_] := Block[{pc}, pc[w_] := n! / Times @@ ((Length /@ Split@w)!); Sum[Total[pc /@ IntegerPartitions[p, {n}, Range@6]], {p, Prime@ Range@ PrimePi[6*n]}]]; Array[a, 20] (* Giovanni Resta, Apr 06 2013 *)

PROG

(PARI) a(n, s=0)=forvec(v=vector(n, i, [1, 6]), isprime(sum(i=1, n, v[i])) && s++); s \\ Illustrative purpose only, impractical for n>>7.

CROSSREFS

Sequence in context: A055837 A124543 A007142 * A190010 A151326 A063000

Adjacent sequences:  A224394 A224395 A224396 * A224398 A224399 A224400

KEYWORD

nonn

AUTHOR

M. F. Hasler, Apr 05 2013

EXTENSIONS

a(11)-a(23) from Giovanni Resta, Apr 06 2013

STATUS

approved

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Last modified April 19 01:20 EDT 2021. Contains 343099 sequences. (Running on oeis4.)